Left to right: Professor Zhang Baile, Liu Guigeng, and Associate Professor Chong Yidong. Photo credit: Nicholas Ang.
In a small laboratory crammed with computers and electronic equipment, a team of physicists is working to develop revolutionary materials that were once the stuff of dreams. Researchers in NTU’s School of Physical and Mathematical Sciences, led by Professor Zhang Baile and Associate Professor Chong Yidong, have been studying photonic metamaterials: synthetic materials in which electromagnetic waves take the place of electric currents. In a paper published in Nature in September 2022, the team announced their latest breakthrough: the realisation of a long-elusive material called a 3D Chern insulator.
The discovery and development of the 3D Chern insulator is the culmination of a multi-year journey for PhD student Liu Guigeng, the first author on the new Nature paper.
A PhD Student’s Scientific Journey
Growing up, Guigeng was fascinated by stories of famous scientists, and dreamed of becoming a scientist himself. As a student at Nankai University in China, he majored in physics and participated in undergraduate research, publishing two scientific papers. Upon graduation, Guigeng jumped at the chance to pursue a PhD at NTU, under the supervision of Professor Zhang Baile and Associate Professor Chong Yidong.
“Studying at NTU was the best decision I ever made,” said Guigeng. “It has been fantastic to work with two talented professors and other fantastic group members.”
Three years have passed since Guigeng started his four-year PhD candidature. During this time, his research has focused on using the mathematical concept of topology to design novel photonic metamaterials.
The Mathematics of Intrinsic Similarities
Topology is a branch of mathematics that deals with how certain fundamental properties of objects do not change when they are stretched, bent, or deformed.
To understand this, imagine a ball and a donut, each made of rubber. Each object cannot be stretched or bent into the other object, absent some kind of disruptive action (e.g., punching a hole into the ball). Mathematicians would therefore say that the ball and the donut are topologically different.
On the other hand, a donut and coffee cup, despite their very different appearances, turn out to be topologically equivalent. A donut can be deformed into a cup, or vice versa, without tearing or punching a hole into it.
Topology is an immensely useful concept in various scientific fields, including biology, data science, and physics. One of its most dramatic manifestations occurs in the physics of materials. Certain materials have energy levels, or “bands”, that can be classified using topology. Since their topological characteristics cannot be easily changed, the properties of these materials are very robust against physical disturbances, such as the introduction of impurities. For this reason, many researchers are exploring the use of topological materials to create devices that are robust to imperfections and environmental disturbances.
First Realisation of Three Dimensional Chern Insulators
Physicists have identified three fundamental topological phases of matter: the quantum Hall insulator, quantum spin Hall insulator, and Chern insulator. Among three dimensional (3D) materials, the quantum Hall insulator and quantum spin Hall insulator have been experimentally realised and thoroughly studied for many years. 3D Chern insulators, however, have proven more elusive, despite a large amount of theoretical work predicting their existence and unique properties.
Guigeng and his co-workers have now achieved a breakthrough by developing the world’s first 3D Chern insulator, using a magnetic photonic crystal.
A photonic crystal is a man-made structure designed to manipulate the properties of electromagnetic waves passing through it. The most striking property of the magnetic photonic crystals studied by Guigeng is that they “break time-reversal symmetry”, meaning that the flow of light looks different if going forward or backward in time. Ordinary media lacks this property; according to previous theoretical studies, the breaking of time-reversal symmetry is necessary for achieving a Chern insulator.
Photograph of the magnetic photonic crystal used to realize a 3D Chern insulator. Photo credit: Liu Guigeng.
Characteristics of 3D Chern Insulators
The team showed that a 3D Chern insulator has several unique characteristics that have never been observed in other classes of materials before.
The band topology of a 3D Chern insulator is described by a quantity called a “Chern vector”. This way of characterising their topology is different from previous topological materials, such as quantum Hall insulators and spin Hall insulators. Using a novel theoretical analysis, Guigeng and his co-workers showed that different choices of Chern vector produce different varieties of 3D Chern insulator, all topologically distinct from one another.
The team also discovered a new type of wave that flows along the two-dimensional (2D) surfaces of any 3D Chern insulator. Similar “topological surface states” have been observed in other topological materials, but the topological surface states of 3D Chern insulators have remarkable features not found anywhere else.
Most strikingly, when the momenta of the topological surface states are measured, they are found to form structures known as torus knots. Similar to the knots that our wired earphones end up tangled in, these torus knots cannot be easily undone. This makes them a powerful experimental signature that can be used to distinguish 3D Chern insulators from other materials.
The team also showed that when two 3D Chern insulators that are topologically inequivalent (i.e., having different Chern vectors) are placed side-by-side, the topological surface states between them form more intricate structures called torus links, consisting of two knots linked together in a way that makes them impossible to separate. Topological surface states in other materials have never been found to possess such features.
Getting Published in a Top Scientific Journal
As one of the world’s foremost multidisciplinary academic journals, the competition for publication in Nature is extremely high. Before a paper can be published, it must be approved by the journal’s editors, as well as undergo rigorous evaluation by peer researchers. Successfully publishing a paper in such a journal is a signature honour for a researcher.
Professor Zhang Baile shared that the peer reviewers on the paper spoke glowingly of their findings. “Our work has two important implications, which were recognised by the reviews,” he said. “First, the demonstration of a long sought-after topological phase, the 3D Chern insulator, is a significant advance in itself. Secondly, our approach opens the door for the development of new kinds of photonic and electronic devices. For example, we can envision 3D photonic circuits that are immune to imperfections introduced during fabrication, or other kinds of disorder.”
Now that the paper has been published, Guigeng is preparing for his PhD graduation. Afterwards, he intends to stay on as a postdoctoral researcher in Professor Zhang’s team, pursuing several ongoing projects.
Asked to reflect on his scientific journey, Guigeng shared that an important characteristic for PhD students is the ability and willingness to collaborate with others. Supervisors and collaborators can provide a great deal of advice and support for PhD students, he notes.
“Another critical thing when pursuing a PhD is to find an important research topic that you are interested in,” says Guigeng. “If you have not found one, do not rush to conduct research on a topic you are not interested in. Try to read as many papers as possible and have frequent discussions with your supervisors and teammates.”
Liu Guigeng. Photo credit: Nicholas Ang.